Why isn't Spin tool or mesh that has been rotated accurate when zooming in
You've just encountered one of the nightmares of doing maths on computers, and it's not a blender bug.
Blender uses floating point numbers internally, and they have finite precision.  This means that when you do complicated calculations like calculating movement through an angle, you only get an approximation of the final answer.
For the majority of uses, the approximations are close enough to the right answer that people don't notice, but you've found one of the rare cases where it does.
If you want to merge the two vertices, select the one that is in the right position, then select the other by holding shift when you left click on it.  Type M to get the merge menu and select &quot;At First&quot;:
select the first vertex with left mouse:

select the second vertex with left mouse while holding shift:

notice that the first vertex is orange.  That means it's the 'active' vertex.
Now type M to bring up the merge menu

and select &quot;At First&quot;